There are really quite a few ways to be independent. I feel like I was able to explore a certain aspects of independence that simply don't come up very often.
The first was decision making independence. Almost every day was a question of which bus to get on, where to go, where to stay, what to do. Being alone lets you make decisions without any thoughts other than your own.
Do you want to walk 10 kilometers today? Do you want to sit on this bench and read for 2 hours? Do you want to take an all night bus? Do you want to eat only almonds and raisins today? Are you going to go through a massive museum in only two and a half hours?
With other people it is quite a bit more difficult to try peculiar things out.
And then there was the responsibility associated with independence. If I got myself into a situation that I couldn't get myself out of, there was no one to get me out. I hiked up a rather large mountain by myself. I don't think it was particularly risky because the entire time I was considering the situation in terms of being all alone.
And the last type of independence is rather peculiar. I would consider it independence of happiness. Are you able to be happy independent of everything else? Regardless of how your body feels, what your situation is, how bored you are, how lost you are, how tired you are, can you be content? I consider this one of the most important forms of independence because once you have it, nothing will ever be able to take it away from you, and it gives you a new sense of life.
The downside of independence is of course loneliness. It's a balancing act that needs to be worked out. A few times on the trip I really got quite lonely, it makes it much easier to appreciate the people in your life when you can leave them for a bit.